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Thursday, August 1, 2013

Readers who follow me on Twitter
will have noticed many tweets on the recent revelations about illegal
NSA surveillance. Here is why I think that none of us in mathematics
and mathematics education can ignore that debate.

There’s a popular conception that
mathematicians are unworldly, and that mathematics is, at its heart,
walled off from the real world, its pursuit a form of escapism that
takes the pursuer into a realm of pure, abstract thoughts.

Certainly, that’s a general sense of
mathematics that I held for many years. Yes, like all my fellow
mathematicians, I always knew that mathematics – all of it –
arose, directly or indirectly, from real world problems, and that any
branch of mathematics having any discipline-internal significance
almost always turns out to have real-world applications. But neither
of those was why I did mathematics. For most of my life as a
mathematician, I simply did not care about the history or application
of what I was doing. It was all about the chase – the search for
new knowledge in a beautiful domain.

Early on in my career, when more
politically active colleagues urged me to boycott conferences and
workshops funded by NATO (a big issue back in the 1970s), or to avoid
applying for research funds from commercial or military sources, I
essentially turned a deaf ear to what they were saying, and got on
with the work that interested me.

As a mathematician working in axiomatic
set theory, with particular foci on the properties of sets of large
infinite cardinality and on undecidability proofs, I felt fairly
confident that nothing I did would ever find practical application,
so for me the issue was purely one of where the money came from to
support my research. I felt “clean,” and not under any moral
pressure regarding potential unethical uses being made of my work.

True, I was aware that the famous early
twentieth century mathematician G. H. Hardy had made the same claim
about his work in number theory, yet in the mid-1970s his work found
highly significant application in the design of secure cryptographic
systems. But I felt that a similar outcome was unlikely in the case
of infinitary set theory. (I am no longer quite as sure about that; I
speculated about possible applications of Cantor’s set theory in my
June
column.)

I think we all have to address the
morality-of-possible-applications question about our work as
mathematicians at one time or another. Some, from Archimedes to Alan
Turing, have actively engaged in military research; others try to
avoid any direct contact with commercial or warfare-related
activities.

The rise of math-based corporations
such as Google that form a large and influential part of today’s
global world, and the closely related growth of the modern,
math-driven security state, as iconicized by the NSA, make it
impossible to maintain any longer the fiction (for such it always
was) that we can pursue mathematics as a pure activity, separate from
applications, be they good or ill.

The uncomfortable fact is, we are in no
different a situation than manufacturers of sporting guns who deny
any agency when their product is used to kill people. (Yes, people
pull the trigger, but as comedian Eddie Izzard pointed
out, “the gun helps.”)

If we want to be able to maintain that
our work will not play a role in someone’s death, torture, or
incarceration – or in someone else achieving enormous wealth and
power – our only option is to not go into mathematics in the first
place. The subject is simply way too powerful as a force – for good
or for evil.

Shortly after September 11, 2001, I was
asked to join a research project funded by the U.S. intelligence
service. For me, that was my crunch time. The work that led to that
invitation was an outgrowth (described in my 1995 book Logic
and Information) of my earlier research in
mathematical logic and set theory. Like it or not, I was already in
deep. To say no to that invitation would have been every bit a
positive action as to say yes. Sitting on the fence was not a
possibility. I was a mathematician. I’d already made the gun.

As the Google founders Larry Page and
Sergei Brin eventually discovered, “Do no evil” is a wonderful
grounding principle, but the power of mathematics renders it an
impossible goal to achieve. The best we can do is try to make our
voice heard, as many mathematicians and nuclear physicists did during
the Cold War, who spoke publicly about the massive scale of the
danger raised by nuclear weapons.

Finding out (as I have over the past
few weeks) that the work I’d done over the past twelve years –
for various branches of the U.S. government (intelligence and military)
and for commercial enterprises (in my case, the video game industry)
– was part of a body of research that had been subverted (as I see
it) to create a massive global surveillance framework, I felt I could
not remain silent.

Not because I felt that I, as an
individual, did anything of significance. I worked on non-classified
projects, and made no major breakthroughs. I was a very tiny cog in a
very big machine. (If “they” are keeping an eye on me, they are
definitely wasting our tax dollars!)

But I did take the money and I did do
the work. I don’t regret doing so. The fact is, I’d made the
crucial choice long before 2001; back in my youth when I decided to
become a mathematician.

Those of us in mathematics education
have always told our students that math is useful. In today’s world
more than ever, we cannot at the same time pretend it is free of
moral issues. Agnosticism is not an option (if it ever really was).
To say or do nothing is inescapably a positive act, just as
significant as saying or doing something.

We humans have created our mathematics,
and used it to help shape our world. Now we have to live in it. Not
only are we the ones who bear a large responsibility for that world,
we are also, by our very expertise, the ones who (in many fundamental
ways) understand it best. (It often seems that only the
mathematically sophisticated really appreciate that an American is
more likely to die in his or her bathtub than from a terrorist
attack, and that more people died on the roads due to increased
traffic during the time after 9/11 when all flights were grounded
than did in the Twin Towers attack.)

So, to return to the question implicit
in my title, “What is mathematics used for?” Douglas
Adams provided the answer: “Life, the
universe, everything.” With such reach and power comes responsibility.

FOOTNOTE: For a more personal take on
the above issues, see the interview
I did on June 21 on Shecky Riemann’s Math Tango blog.

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The Mathematical Association of America is the world's largest community of mathematicians, students, and enthusiasts. We accelerate the understanding of our world through mathematics, because mathematics drives society and shapes our lives. Visit us at maa.org.